Using the idea of piecewise functions, create an appropriate scale on axes and design a rollercoaster, using technology like Graph. The rollercoaster must have the features listed below.

a) Uses at least four different polynomial functions, pieced together.
b) Models the maximum height of 132 feet and the initial drop of 130 feet (39.624 metre).
c) Has at least 4 other drops.
d) Goes through an underground tunnel at least once (assuming y = 0 is the ground)
e) Any other features you feel would add to the ride and can be modeled with a polynomial function.

Try to make each of the polynomial functions flow into one another to create a smooth ride for your passengers. To prevent functions from overlapping, make sure to restrict the domain of the function. Set each polynomial function to a different color.

For each of the pieces in the design:

a) State the equation for the polynomial function used.
b) Determine the degree of the function.
c) State the domain and range of the restricted function.
d) Determine if each unrestricted function pieces have even or odd symmetry, or neither. If neither, determine which transformations, if any, could be applied to make it even or odd over its unrestricted domain?

Take the first three pieces of your rollercoaster and model them with a single function and answer the following questions:

a) If you represent these three pieces with a single function, what degree do you think this function will be? Justify your reasoning.
b) Determine an equation for this function.
c) Graph the equation you created together with the first three functions. How similar is it? If there are any differences, why do you believe that is?